Um, here I have a Probability Question, but I'm not completely sure where to even begin:
Given that the pass rate of an entrance exam for a Mathematics program is 55%, what is the probability that a student fails it the first two times and passes it the third time?
here. Probability that he fails first test is 1-0.55 = 0.45. Probability of failing second test is again 0.45. Probability of passing third test is 0.55. Multiply them. Note that I assumed at the beginning that the events are independent.